Precalculus Examples

$\frac{1}{5} \cdot (\log_{4} (x) + \log_{4} (7)) - \log_{4} (y)$

Step 1

Simplify each term.

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Step 1.1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\frac{1}{5} \cdot \log_{4} (x \cdot 7) - \log_{4} (y)$

Step 1.2

Move $7$ to the left of $x$ .

$\frac{1}{5} \cdot \log_{4} (7 \cdot x) - \log_{4} (y)$

Step 1.3

Simplify $\frac{1}{5} \log_{4} (7 x)$ by moving $\frac{1}{5}$ inside the logarithm.

$\log_{4} ({(7 x)}^{\frac{1}{5}}) - \log_{4} (y)$

Step 1.4

Apply the product rule to $7 x$ .

$\log_{4} (7^{\frac{1}{5}} x^{\frac{1}{5}}) - \log_{4} (y)$

Step 2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{4} (\frac{7^{\frac{1}{5}} x^{\frac{1}{5}}}{y})$